1. Field of the Invention
The field of invention is vibration control devices and the means to control these devices, which are employed to protect structures from the destructive forces of earthquake, high winds, and the like.
2. Description of Related Art
Examples of vibration control devices of the dynamic damper type (DD) in the subject field of invention are illustrated in Japanese Patent Laid-open No. 63-76932 and Japanese Patent Publication No. 3-38386.
Prior art FIG. 10 of the subject application shows a vibration model of a DD applied to a structure, wherein m.sub.1 is a mass of a main body of the structure, constituting a main vibration system, and m.sub.d is a mass of an additional mass body constituting a damping system. The spring constant of the main body of the structure is identified as k.sub.1. The main body of the structure and the additional mass body are connected by means of a spring having a spring constant k.sub.d and a damper having a damping coefficient c.sub.d. Displacement of the mass m.sub.1 is indicated by the arrow x.sub.1, and counter displacement of mass m.sub.d is indicated by the arrow x.sub.d.
A natural angular frequency of the main vibration system is given by: EQU .omega..sub.1 =(k.sub.1 /m.sub.1 ).sup.1/2
The mass m.sub.d of the damping system is normally designed so that the ratio of the mass m.sub.d to the mass m.sub.1 of the main vibration system may be set to approximately become: EQU .mu.=m.sub.d /m.sub.1 .gtoreq.0.01
At this time, the natural angular frequency of the damping system is given by: EQU .omega..sub.d =(1/1+.mu.).omega..sub.1
A damping coefficient c.sub.d and a damping factor h.sub.d are represented by the following equations, respectively:
c.sub.d =2 m.sub.d .omega..sub.d h.sub.d PA1 h.sub.d =[3.mu./8(1+.mu.)].sup.1/2
There are also active mass drivers (AMD) which function as vibration control devices, e.g. , U.S. Pat. No. 5,022,201 (Japanese Patent Laid-open Nos. 1-275866, 1-275867, 1-275868, and 1-275869.
Prior art FIG. 11 shows a vibration model of an AMD which applies a control force u(t) by means of hydraulic power or electromagnetic force of an actuator positioned between the main body of the structure having a mass m and the additional mass body having a mass m.sub.d, to actively control the vibration of the structure.
In the prior art control device of FIG. 11, assuming that a spring between the main body of the structure and the additional mass body constituting a vibration control device is set pursuant to the equation EQU .omega..sub.d .ltoreq.(1/2).omega..sub.1,
the control force u(t) is given by the following equation: EQU u(t)=G.sub.1 (dx.sub.1 /dx)+G.sub.2 (dx.sub.d /dt)
wherein G.sub.1 is a gain in a circuit including an automatic gain control circuit (AGC) or the like against the response speed of the structure and attains the correspondences of large inputs through small inputs, wherein G.sub.2 becomes a negative value. The second term in the above equation gives a damping property to the additional mass body and attains a stability thereof by adding the product of a gain G.sub.2 and vibration speed to the control force of the additional mass body.
As shown in prior art FIG. 12, a spring having a spring constant k.sub.d is added to the AMD described above, in parallel with the control force u(t) to obtain a vibration control effect by means of less control force in comparison with that of an active tuned mass damper (designated as ATMD hereafter. )
In an ATMD, a spring constant k.sub.d is set so that the vibration of an additional mass body may synchronize with that of a structure, that is, EQU .omega..sub.d =.omega..sub.1
and the control force u(t) is, for example, given by the following equation, EQU u(t)=G.sub.1 (dx.sub.1 /dt)+G.sub.2 (dx.sub.d /dt)+G.sub.3 (x.sub.1 -x.sub.d)
wherein G.sub.3 is a gain having a negative sign and cancels a part of the inertial force applied to the additional mass body at a vibration time due to the third term in the above equation, so that the additional mass body may be vibrated by less control force.
Japanese Patent Publication No. 3-70075 discloses a vibration control device of an active type for controlling structural vibration due to an earthquake or the like. A second additional mass body having a mass less than the first additional mass body of the DD is connected to the first additional mass body of the DD through a spring and an actuator, wherein a control force is applied to the second additional mass body by the actuator.
In the above-mentioned vibration control device, the DD has an advantage in that no energy supply to the device is necessary. The vibration control effect is determined by the mass ratio of the first additional mass body to the mass of the structure. Therefore, it is necessary to have a large first additional mass body with which it is difficult to obtain a sufficient vibration control.
In the case of the AMD, more control can be expected by the use of an additional mass body having a small mass in comparison with that in the case of the DD. However, an energy supply is necessary, and it is necessary to arrange additional facilities and equipment for the energy supply. These additional facilities include a specially designed control circuit for applying a predetermined control force in accordance with the vibration responses of the structure and the additional mass body; means to secure stability of the device; and means to prevent malfunction of the device.
As described above, the ATMD has an advantage in that the control force can be lessened in comparison with that in the case of the AMD, but it takes time to synchronize the vibration of the additional mass body with the vibration of the structure EQU (.omega..sub.d =.omega..sub.1)
Furthermore, in the ATMD a portion of the inertial force can be canceled by providing a term corresponding to the spring force in order to obtain a large control effect by less control force. However, there is a problem in that a synchronizing period is newly generated for a period longer than the natural period of the structure in the periodic components of the earthquake, wherein the amplitude of the additional mass body increases so that control becomes difficult.